# A Family of Bidirectional DC–DC Converters for Battery Storage System with High Voltage Gain

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Bidirectional DC–DC Converters with Wide Voltage Conversion Ratio

_{1}, Q

_{2}, and Q

_{3}; capacitors C

_{1}, C

_{2}, and C

_{3}(I and II), in addition, there are two inductors L

_{1}and L

_{2}in these converters. The proposed converters are analyzed based on the assumption that the converters operate in continuous conduction mode (CCM), and that all the components are analyzed in the ideal condition.

#### 2.1. Construction of the Converter I

_{1}is shown as the main power switch, and Q

_{2}and Q

_{3}are shown as the synchronous rectifiers. The gate signal of Q

_{1}is complementary to Q

_{2}and Q

_{3}; thus, d

_{1}= 1 − d

_{2}= 1 − d

_{3}= d

_{Boost}. The topological states are described in Figure 5a,b.

_{0}–t

_{1}]: When the circuit operates in this case. Switch Q

_{1}is turned ON, and switches Q

_{2}and Q

_{3}are turned OFF, as described in Figure 5a, the battery voltage flows through inductor L

_{1}, while inductor L

_{2}and C

_{3}are charging through C

_{2}. With reference to Figure 5a, in addition, by applying the Kirchhoff voltage law (KVL) and Kirchhoff current law (KCL) to the circuit, the formulas below are obtained for this state.

_{L}

_{1}, U

_{L}

_{2}represent the voltage on the inductors. U

_{C}

_{1}, U

_{C}

_{2}and U

_{C}

_{3}are the voltage on the capacitors. U

_{high}and U

_{low}are shown as the voltage on the DC bus side and battery side. I

_{high}and I

_{low}are shown as the current on the DC bus side and battery side. These symbols are applicable to all of the converters in this paper.

_{1}–t

_{2}]: By contrast, the second topological state is depicted in Figure 5b. In this case, the input voltage and the indictor L

_{1}are discharged to capacitor C

_{2}in series. Moreover, inductor L

_{2}is also discharged to C

_{1}through Q

_{3}, and C

_{2}is charged through Q

_{2}. The output voltage is boosting by connecting the capacitors C

_{1}and C

_{2}in stack. With reference to Figure 5b, by applying the same principle, the formulas below are derived for this state.

_{1}and L

_{2}on the basis of (1) and (3), the voltage gain rate M

_{Boost}of suggested converter I in CCM can be expressed as

_{1}and C

_{2}can be written as

_{L}

_{1}and I

_{L}

_{2}can be achieved as

_{1}is complementary to Q

_{2}and Q

_{3}; thus, d

_{1}= 1 − d

_{2}= 1 − d

_{3}= d

_{Buck}. The topological stages are depicted in Figure 6a,b.

_{0}–t

_{1}]: When Q

_{1}is turned OFF, and Q

_{2}and Q

_{3}are turned ON. The switching state is presented in Figure 6a. As for this state, L

_{1}, L

_{2}, and C

_{3}are charged by C

_{1}and C

_{2}, respectively, through Q

_{2}and Q

_{3}. The following formulas are derived for this state.

_{1}–t

_{2}]: In this state, switching state is opposed to previous operation. The switching state is presented in Figure 6b. In this case, C

_{3}and L

_{2}are in series connection to charge C

_{2}by Q

_{1}. Moreover, L

_{1}also discharges to C

_{0}through Q

_{1}, on the basis of Figure 6b. The formulas below are then calculated for this case.

_{1}and L

_{2}according to Equation (8) and Equation (10), the boost conversion M

_{Boost}of the proposed converter I in CCM can be obtained as

_{L}

_{1}and I

_{L}

_{2}of inductors L

_{1}and L

_{2}can be obtained as

#### 2.2. Construction of Presented Converter II

_{1}is ON, and Q

_{2}and Q

_{3}are turned OFF. The symbolic representation is the same as the converter I. In light of Figure 7a, by using the KVL and KCL laws to the circuit, the following equations based on this state can be formed as

_{1}and L

_{2}according to Equations (17) and (19), the voltage gain M

_{Boost}of the proposed converter II in CCM can be obtained as

_{1}and C

_{2}can be expressed as

_{L}

_{1}and I

_{L}

_{2}on the inductors L

_{1}and L

_{2}can be expressed as

_{0}–t

_{1}]: This operating mode is effective when the power switch Q

_{1}is OFF and Switches Q

_{2}and Q

_{3}are ON. The inductors L

_{1}and L

_{2}are in charging mode while capacitor C

_{3}is discharging. In accordance with Figure 8a, by using the KVL and KCL laws to the circuit, the formulas below are derived for this case

_{1}–t

_{2}]: The switching state is reverse to the previous state. Both inductors are in discharge mode, and Capacitors C

_{1}and C

_{3}are charged by the current that flows through the inductor L

_{2}. Similarly, from Figure 8b, the following equations is derived.

_{Boost}and voltage stresses on the capacitors of the proposed Converter II in CCM can be expressed as

_{L}

_{1}and I

_{L}

_{2}on inductors L

_{1}and L

_{2}can be obtained as

#### 2.3. Construction of the Proposed Converter III

_{1}and Q

_{2}are turned ON, Q

_{3}is turned OFF, thus, d

_{1}= d

_{2}= 1 − d

_{3}= d

_{Boost}. The switching states are depicted in Figure 10a,b.

_{1}and Q

_{2}are turned ON, and switch Q

_{3}is turned OFF. By the detailed analysis about Reference [24], the voltages stresses across L

_{1}and L

_{2}can be expressed as

_{1}and L

_{2}can be expressed as

_{1}and L

_{2}, the voltage gain can be expressed as

_{1}, Q

_{2}, and Q

_{3}can be expressed as

_{1}–Q

_{3}can be expressed as

_{1}is complementary to Q

_{2}and Q

_{3}; thus, d

_{3}= 1 − d

_{1}= 1 − d

_{2}= d

_{Buck}. The topological states are presented in detail in Figure 11a,b.

_{0}–t

_{1}]. When switch Q

_{3}is ON, and Switches Q

_{1}and Q

_{2}are OFF, the switching state is presented in Figure 11a. DC bus voltage is charging the inductors L

_{1}and L

_{2}, and the output capacitor C

_{o}discharging energy to the load. Consequently, it can be calculated that

_{1}–t

_{2}]. In this state, switching state is opposed to previous operation. The equivalent current flow circuit is shown in Figure 11b. The battery voltage, inductors L

_{1}and L

_{2}are discharging energy to the output capacitor C

_{o}and the load. Therefore, voltage stresses across inductors L

_{1}and L

_{2}can be expressed as

_{1}and L

_{2}, the voltage gain can be expressed as

#### 2.4. Voltage and Current Ripple Calculation of the Proposed Converters

_{L}) on the inductance is calculated by

_{c}) can be obtained from the output capacitor.

_{1}and L

_{2}about proposed converter III are equal to the boost converter because of the similar topological states.

_{c}). That means converter I and II are easier to select the output capacitor due to the small voltage ripple.

#### 2.5. Comparisons with Conventional Converters

_{l}represent as the inductor parasitic resistance, R is the load resistance.

_{l}is set to 0.01, the voltage gain ratio can be obtained under different duty cycle.

#### 2.6. Efficiency and Power Loss Calculation

_{ds}is the conduction resistance, t

_{r}and t

_{f}represent the rise time and fall time of the switch.

_{win}is the ac resistance of the windings. k

_{i}, α, and β are empirical constants determined by the core material characteristic. k

_{i}= 0.33, α = 1.98, and β = 1.64. f, B, and V are operating frequency, flux density and volume of the core [26].

_{extra_L}represent the extra loss of the converters.

## 3. Experiment Results

#### 3.1. Experimental Results in the Boost/Buck Mode

_{in}= 40 V, V

_{o}= 250 V, f

_{s}= 25 KHz, and P

_{o}= 200 W; experimental results with respect to converter I are presented in Figure 16.

_{1}, Q

_{2}and Q

_{3}in the boost mode are presented in Figure 16a. It can be seen that the voltage stresses on Q

_{1}–Q

_{3}are approximately 150 V, which indicates that the voltage stresses on Q

_{1}–Q

_{3}are equal to V

_{high}/(1 + D). Under the same situation, Figure 16c shown the inductors current under the boost mode.

_{2}and Q

_{3}, and Q

_{1}in buck mode are presented in Figure 16b. It can be revealed that the voltage stresses on Q

_{1}–Q

_{3}are approximately 150 V, which indicates that the voltage stresses on Q

_{1}–Q

_{3}are equal to V

_{high}/(1 + D). Under the same conditions, Figure 16d shown the inductors current under the buck mode.

_{1}and L

_{2}are lower than those of the converters in [22], which makes it easier to design inductance.

_{1}and Q

_{2}, and Q

_{3}in the boost mode are presented in Figure 17a. The voltage stresses on Q

_{1}–Q

_{2}are 150 V, which indicates that the voltage stresses on Q

_{1}–Q

_{3}are equal to (V

_{o}+ V

_{in})/2. On the other hand, the voltage stress on Q

_{3}is 300 V, which indicates that the voltage stresses on Q

_{3}are equal to V

_{o}+ V

_{in}. Under the same situation, Figure 17c shown the inductors current under the boost mode.

_{2}and Q

_{3}, and Q

_{1}in buck mode are presented in Figure 17b. The voltage stresses on Q

_{1}–Q

_{2}are 150 V, which indicates that the voltage stresses on Q

_{1}–Q

_{2}are equal to (V

_{o}+ V

_{in})/2. On the contrary, the voltage stress on Q

_{3}is 300 V, which indicates that the voltage stresses on Q

_{3}are equal to V

_{o}+ V

_{in}. Under the same conditions, Figure 17d shown the inductors current under the buck mode.

_{1}and L

_{2}are identical because of the same operating mode.

#### 3.2. Measured Efficiency Analysis of the Converters

#### 3.3. Power Loss Distribution Analysis of Proposed Converters

_{low}= 120 V, U

_{high}= 250 V, and P

_{o}= 200 W. When the suggested converters operate in boost mode, the comparison of loss analysis is presented in Figure 20a. According to analyzing results of the power losses distribution, the maximum power loss is calculated as 20.95 W, which is due to Converter III. It can be convinced that the dominant sources of power losses are due to the switching losses, which account for 25%, 26%, and 30% of the total losses, respectively. In case of the presented converters operate in buck mode, the loss distribution is presented in Figure 20b. By analyzing the distribution of power losses, the maximum power loss is found to be 20.4 W, which is due to Converter III. It can be maintained that the dominant sources of power losses are due to the switching losses.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Yilmaz, M.; Krein, P.T. Review of battery charger topologies, charging power levels, and infrastructure for plug-in electric and hybrid vehicles. IEEE Trans. Power. Electron.
**2013**, 28, 2151–2169. [Google Scholar] [CrossRef] - Han, Y.; Chen, W.; Li, Q. Energy Management Strategy Based on Multiple Operating States fora Photovoltaic/Full Cell/Energy Storage DC Microgrid. Energies
**2017**, 10, 136. [Google Scholar] [CrossRef] - Hong, C.M.; Yang, L.S.; Liang, T.J.; Chen, J.F. Novel bidirectional DC–DC converter with high step-up/down voltage gain. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), San Jose, CA, USA, 20–24 September 2009; pp. 60–66. [Google Scholar]
- Zhang, Y.; Gao, Y.; Li, J.; Sumner, M. Interleaved switched-capacitor bidirectional DC-DC converter with wide voltage-gain Range for energy storage systems. IEEE Trans. Power Electron.
**2018**, 33, 3852–3869. [Google Scholar] [CrossRef] - Inoue, S.; Akagi, H.S. A bidirectional isolated dc–dc converter as a core circuit of the next-generation medium-voltage power conversion system. IEEE Trans. Power Electron.
**2007**, 22, 535–542. [Google Scholar] [CrossRef] - Chao, K.-H.; Huang, C.-H. Bidirectional dc–dc soft-switching converter for stand-alone photovoltaic power generation systems. IET Power Electron.
**2014**, 7, 1557–1565. [Google Scholar] [CrossRef] - Shen, C.-L.; Shen, Y.-S.; Tsai, C.-T. Isolated DC-DC Converter for Bidirectional Power Flow Controlling with Soft-Switching Feature and High Step-Up/Down Voltage Conversion. Energies
**2017**, 10, 296. [Google Scholar] [CrossRef] - Liu, C.; Chau, K.T.; Wu, D.; Gao, S. Opportunities and challenges of vehicle-to-home, vehicle-to-vehicle, and vehicle-to-grid technologies. Proc. IEEE
**2013**, 101, 2409–2427. [Google Scholar] [CrossRef] - Grbovic, P.J.; Delarue, P.; Moigne, P.L.; Bartholomeus, P. A bidirectional three-level dc-dc converter for the ultra-capacitor applications. IEEE Trans. Ind. Electron.
**2010**, 57, 3415–3430. [Google Scholar] [CrossRef] - Lai, C.M.; Lin, Y.C.; Lee, D.S. Study and implementation of a two-phase interleaved bidirectional DC/DCconverter for vehicle and dc-microgrid systems. Energies
**2015**, 8, 9969–9991. [Google Scholar] [CrossRef] - Jin, K.; Yang, M.; Ruan, X.; Xu, M. Three-level bidirectional converter for fuel-cell/battery hybrid power system. IEEE Trans. Ind. Electron.
**2010**, 57, 1976–1986. [Google Scholar] [CrossRef] - Liang, T.J.; Liang, H.H.; Chen, S.M.; Chen, J.F.; Yang, L.S. Analysis, design, and implementation of a bidirectional double-boost DC-DC converter. IEEE Trans. Ind. Appl.
**2014**, 50, 3955–3962. [Google Scholar] [CrossRef] - Fang, X.; Ji, X. Bidirectional power flow Z-source dc-dc converter. In Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC), Harbin, Hei Longjiang, China, 3–5 September 2008; pp. 1–5. [Google Scholar]
- Kim, I.D.; Paeng, S.H.; Ahn, J.W.; Nho, E.C.; Ko, J.S.I. New bidirectional ZVS PWM Sepic/Zeta DC–DC converter. In Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE), Vigo, Spain, 4–7 June 2007; pp. 17–22. [Google Scholar]
- Li, C.; Herrera, L. Design and implementation of a bidirectional isolated Cuk converter for low-voltage and high-current automotive DC source applications. IEEE Trans. Veh. Technol.
**2014**, 63, 2567–2577. [Google Scholar] [CrossRef] - Lee, H.Y.; Liang, T.J.; Chen, J.F.; Chen, K.H. Design and implementation of a bidirectional SEPIC-Zeta DC-DC Converter. In Proceedings of the IEEE International Symposium on Circuit and Systems (ISCAS), Melbourne, Australia, 1–5 June 2014; pp. 101–104. [Google Scholar]
- Liang, T.J.; Lee, J.H. Novel-high-conversion-ratio high efficiency isolated bidirectional DC-DC converter. IEEE Trans. Ind. Electron.
**2015**, 62, 4492–4503. [Google Scholar] [CrossRef] - Lin, C.C.; Yang, L.S.; Wu, G.W. Study of a non-isolated bidirectional DC-DC converter. IET Power Electron.
**2013**, 6, 30–37. [Google Scholar] [CrossRef] - Fardoun, A.A.; Ismail, E.H.; Sabzali, A.J.; Al-Saffar, M.A. Bidirectional converter with low input/output current ripple for renewable energy applications. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), Phoenix, AZ, USA, 17–22 September 2011; pp. 3322–3329. [Google Scholar]
- Ahmad, A.; Singh, R.K.; Mahanty, R. Bidirectional quadratic converter for wide voltage conversion ratio. In Proceedings of the IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Trivandrum, India, 14–17 December 2016; pp. 1–5. [Google Scholar]
- Banaei, M.R.; Bonab, H.A.F. A novel structure for single-switch nonisolated transformerless buck–boost DC–DC converter. IEEE Trans. Ind. Electron.
**2017**, 64, 198–205. [Google Scholar] [CrossRef] - Zhang, Y.; Liu, Q.; Li, J.; Sumner, M. A Common Ground Switched-Quasi-Z-Source Bidirectional DC–DC Converter With Wide-Voltage-Gain Range for EVs with Hybrid Energy Sources. IEEE Trans. Ind. Electron.
**2018**, 65, 5188–5200. [Google Scholar] [CrossRef] - Pires, V.F.; Foito, D.; Batista, F.R.B.; Silva, J.F. A photovoltaic generator system with a DC/DC converter based on an integrated Boost-Cuk. Sol. Energy
**2016**, 136, 1–9. [Google Scholar] [CrossRef] - Yang, L.S.; Liang, T.J.; Chen, J.F. Transformerless DC–DC converters with high step-up voltage gain. IEEE Trans. Ind. Electron.
**2009**, 56, 3144–3152. [Google Scholar] [CrossRef] - Gules, R.; Meneghette, W.; Reis, E.; Romaneli, E.; Badin, A. A modified SEPIC converter with high static gain for renewable applications. IEEE Trans. Power Electron.
**2014**, 29, 5860–5871. [Google Scholar] [CrossRef] - Ramezani, A.; Farhangi, S.; Iman-Eini, H.; Farhangi, B.; Rahim, R. Optimized LCC-Series compensated Resonant Network for Stationary Wireless EV Chargers. IEEE Trans. Ind. Electron.
**2019**, 66, 2756–2765. [Google Scholar] [CrossRef]

**Figure 5.**Topological states of the converter I in boost mode. (

**a**) [t

_{0}–t

_{1}]. (

**b**) [t

_{1}–t

_{2}].

**Figure 11.**Topological states of Converter III in the buck mode. (

**a**) [t

_{0}–t

_{1}]. (

**b**) [t

_{1}–t

_{2}].

**Figure 12.**Voltage gain ratio comparison between proposed converters and conventional converters with parasitic resistance.

**Figure 13.**Efficiency comparison of the proposed converters and traditional converters. (

**a**) traditional converters; (

**b**) proposed converters.

**Figure 16.**Experimental results: (

**a**) voltage stress across Q

_{1}–Q

_{3}in boost mode, (

**b**) voltage stress across Q

_{1}–Q

_{3}in buck mode, (

**c**) inductor current in boost mode, and (

**d**) inductor current in buck mode.

**Figure 17.**Experimental results: (

**a**) voltage stress across Q

_{1}–Q

_{3}in boost mode, (

**b**) voltage stress across Q

_{1}–Q

_{3}in buck mode, (

**c**) inductor current in boost mode, and (

**d**) inductor current in buck mode.

**Figure 18.**Efficiencies of proposed converters in boost and buck modes with U

_{high}= 250 V, U

_{low}= 40–130 V, and P

_{o}= 200 W.

**Figure 20.**Calculated power loss distributions with U

_{low}= 120 V, U

_{high}= 250 V, and P

_{o}= 200 W: (

**a**) boost mode and (

**b**) buck mode.

Topology | Converter I | Converter II | Converter III | Buck-Boost | SEPIC | Ćuk |
---|---|---|---|---|---|---|

Input current | Continuous | Continuous | Discontinuous | Discontinuous | Continuous | Continuous |

Switch voltage stress | V_{high}/(1 + D_{Boost}) ^{1}V _{high}/(2 − D_{Buck}) ^{2} | V_{high}/(1 + D_{Boost}) ^{1}V _{high}/(2 − D_{Buck}) ^{2} | (V_{low} + V_{high})/2 ^{3}V _{low} + V_{high} ^{4} | V_{in} | V_{in} | V_{in} |

Voltage gain ratio | (1 + D)/(1 − D) D/(2 − D) | (1 + D)/(1 − D) D/(2 − D) | (1 + D)/(1 − D) D/(2 − D) | D/(1 − D) | D/(1 − D) | D/(1 − D) |

Common ground | YES | NO | YES | YES | YES | YES |

Num. of switches | 3 | 3 | 3 | 1 | 1 | 1 |

Num. of inductors | 2 | 2 | 2 | 1 | 2 | 2 |

Voltage Ripple | $\frac{{V}_{high}\cdot D}{2\ast R\cdot f\cdot C}$ | $\frac{{V}_{high}\cdot D}{2\ast R\cdot f\cdot C}$ | $\frac{{V}_{high}\cdot D}{R\cdot f\cdot C}$ | $\frac{{V}_{high}\cdot D}{R\cdot f\cdot C}$ | $\frac{{V}_{high}\cdot D}{R\cdot f\cdot C}$ | $\frac{{V}_{high}\cdot D}{R\cdot f\cdot C}$ |

Current Ripple | $\frac{{V}_{low}\cdot D}{L\cdot f}$ | $\frac{{V}_{low}\cdot D}{L\cdot f}$ | $\frac{{V}_{low}\cdot D}{L\cdot f}$ | $\frac{{V}_{low}\cdot D}{L\cdot f}$ | $\frac{{V}_{low}\cdot D}{L\cdot f}$ | $\frac{{V}_{low}\cdot D}{L\cdot f}$ |

^{1}Switch voltage stress in Boost mode.

^{2}Switch voltage stress in Buck mode.

^{3}Switch voltage stress on Q

_{1}and Q

_{2}.

^{4}Switch voltage stress on Q

_{3}.

Parameters | Symbol | Value |
---|---|---|

Battery voltage | V_{low} | 40–130 [Vdc] |

Output voltage | V_{high} | 250 [Vdc] |

Inductor | L_{1}L_{2} | 102 [uH] |

Output Capacitor | C_{1}C_{2} | 50 [uF] |

Capacitor | C_{3} | 3.37 [uF] |

Output power | P_{O} | 200 [W] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, H.; Chen, Y.; Park, S.-J.; Kim, D.-H.
A Family of Bidirectional DC–DC Converters for Battery Storage System with High Voltage Gain. *Energies* **2019**, *12*, 1289.
https://doi.org/10.3390/en12071289

**AMA Style**

Zhang H, Chen Y, Park S-J, Kim D-H.
A Family of Bidirectional DC–DC Converters for Battery Storage System with High Voltage Gain. *Energies*. 2019; 12(7):1289.
https://doi.org/10.3390/en12071289

**Chicago/Turabian Style**

Zhang, Hailong, Yafei Chen, Sung-Jun Park, and Dong-Hee Kim.
2019. "A Family of Bidirectional DC–DC Converters for Battery Storage System with High Voltage Gain" *Energies* 12, no. 7: 1289.
https://doi.org/10.3390/en12071289